Let's break the problem into steps: --- ## **Step 1: Gather the Data** - **Initial Equipment Cost:** $5,500,000 - **Salvage Value (End of Year 5):** $450,000 - **Depreciation (Straight-line, 5 years to zero):** \[ \text{Depreciation per year} = \frac{\$5,500,000}{5} = \$1,100,000 \] - **Market Research Costs (Sunk Cost):** $250,000 (already paid, ignore for FCF) - **Annual Revenue:** $1,650,000 - **Annual Costs:** $500,000 - **Project Life:** 5 years - **Tax Rate:** 30% - **WACC:** 10.40% --- ## **Step 2: Calculate Annual Operating Cash Flows** ### **a) EBIT Calculation** \[ \text{EBIT} = \text{Revenue} - \text{Costs} - \text{Depreciation} \] \[ \text{EBIT} = \$1,650,000 - \$500,000 - \$1,100,000 = \$50,000 \] ### **b) Tax Calculation** \[ \text{Tax} = \text{EBIT} \times 30\% = \$50,000 \times 0.30 = \$15,000 \] ### **c) Net Operating Profit After Tax (NOPAT)** \[ \text{NOPAT} = \text{EBIT} - \text{Tax} = \$50,000 - \$15,000 = \$35,000 \] ### **d) Add Back Depreciation (Non-cash)** \[ \text{Annual Operating FCF} = \text{NOPAT} + \text{Depreciation} = \$35,000 + \$1,100,000 = \$1,135,000 \] --- ## **Step 3: Calculate Terminal Year (Year 5) Cash Flow** In Year 5, add after-tax salvage value: - **Salvage Value:** $450,000 - **Book Value at End:** $0 (since depreciated to zero) - **Tax on Salvage:** Since Book Value = 0, \[ \text{Tax on Salvage} = (\text{Salvage Value} - \text{Book Value}) \times \text{Tax Rate} = \$450,000 \times 0.30 = \$135,000 \] - **After-tax Salvage Value:** \$450,000 - \$135,000 = \$315,000 **Total Cash Flow in Year 5:** \[ \text{Year 5 FCF} = \$1,135,000 + \$315,000 = \$1,450,000 \] --- ## **Step 4: Lay Out the FCFs** | Year | FCF | |------|-------------| | 0 | -$5,500,000 | | 1-4 | $1,135,000 | | 5 | $1,450,000 | --- ## **Step 5: Calculate NPV** \[ \text{NPV} = \sum \frac{FCF_t}{(1+WACC)^t} \] Where WACC = 10.40% = 0.104 Let's break this down: ### **Discount Factors** - Year 1: \( \frac{1}{1.104^1} = 0.906 \) - Year 2: \( \frac{1}{1.104^2} = 0.821 \) - Year 3: \( \frac{1}{1.104^3} = 0.744 \) - Year 4: \( \frac{1}{1.104^4} = 0.674 \) - Year 5: \( \frac{1}{1.104^5} = 0.611 \) ### **Present Values** - Year 1: $1,135,000 × 0.906 = $1,028,010 - Year 2: $1,135,000 × 0.821 = $932,035 - Year 3: $1,135,000 × 0.744 = $844,440 - Year 4: $1,135,000 × 0.674 = $765,290 - Year 5: $1,450,000 × 0.611 = $885,950 ### **Total PV of Inflows** \[ \text{Total PV} = 1,028,010 + 932,035 + 844,440 + 765,290 + 885,950 = \$4,455,725 \] ### **NPV Calculation** \[ \text{NPV} = \text{Total PV} - \text{Initial Outlay} \] \[ \text{NPV} = \$4,455,725 - \$5,500,000 = -\$1,044,275 \] --- ## **Step 6: Calculate IRR** IRR is the rate that sets NPV = 0: Set up the cash flows: - Year 0: -$5,500,000 - Year 1-4: $1,135,000 - Year 5: $1,450,000 Using a financial calculator or Excel's IRR function: \[ \text{IRR} = \text{IRR}(-5,500,000,\ 1,135,000,\ 1,135,000,\ 1,135,000,\ 1,135,000,\ 1,450,000) \] Let’s estimate IRR by trial (or using Excel): - Trying 0%: NPV = $1,135,000×4 + $1,450,000 = $5,990,000; $5,990,000 - $5,500,000 = $490,000 (NPV positive). - Trying 10%: NPV = as above, -$1,044,275 (negative). - Trying 5%: Discount factors: 0.952, 0.907, 0.864, 0.823, 0.784 Year 1: $1,135,000 × 0.952 = $1,080,520 Year 2: $1,135,000 × 0.907 = $1,029,145 Year 3: $1,135,000 × 0.864 = $980,040 Year 4: $1,135,000 × 0.823 = $934,205 Year 5: $1,450,000 × 0.784 = $1,136,800 Total PV = $5,160,710 NPV = $5,160,710 - $5,500,000 = -$339,290 (still negative). Trying 2%: Factors: 0.980, 0.961, 0.942, 0.924, 0.906 Year 1: $1,135,000 × 0.980 = $1,112,300 Year 2: $1,135,000 × 0.961 = $1,091,435 Year 3: $1,135,000 × 0.942 = $1,070,670 Year 4: $1,135,000 × 0.924 = $1,048,740 Year 5: $1,450,000 × 0.906 = $1,313,700 Total PV = $5,636,845 NPV = $5,636,845 - $5,500,000 = $136,845 (now positive). So, between 2% and 5%. Let's interpolate: At 2%: NPV = $136,845 At 5%: NPV = -$339,290 So IRR ≈ 2% + [($136,845)/($136,845 + $339,290)] × (5%-2%) ≈ 2% + [($136,845)/$476,135] × 3% ≈ 2% + 0.287 × 3% ≈ 2.86% So, **IRR ≈ 2.9%** --- ## **Step 7: Decision** - **NPV = -$1,044,275** (negative) - **IRR ≈ 2.9%** (much less than WACC 10.4%) **Conclusion:** Reject the project, because the NPV is negative and the IRR is less than the required rate of return (WACC). --- ## **Step 8: Other Considerations** - **Sunk Costs:** Market research costs are irrelevant (already incurred). - **Sensitivity Analysis:** What if revenues or costs are different? - **Strategic value:** Does the project provide other benefits (market entry, learning, etc.)? - **Alternative Use of Capital:** Is there a better option for this investment? - **Risk Factors:** Are forecasted revenues/costs reliable? Are there risks not captured in the base-case? --- ## **Final

Based on the detailed analysis above, the final conclusion is: ### **Final Answer:** - **Net Present Value (NPV):** Approximately **-\$1,044,275** - **Internal Rate of Return (IRR):** Approximately **2.9%** Since the NPV is negative and the IRR is significantly below the company's WACC of 10.4%, **FUN should reject the project**. --- ### **Additional considerations:** 1. **Sunk Costs:** The \$250,000 market research costs are sunk and should not influence the decision. 2. **Risk and Uncertainty:** The analysis assumes stable revenues and costs; any variation could further impact profitability. 3. **Strategic Benefits:** If the project offers strategic advantages (e.g., market entry, technological capability), these should be weighed separately. 4. **Alternative Investments:** The company should compare this project's return with other potential projects or investments to ensure optimal capital allocation. 5. **Financial and Non-Financial Factors:** Consider potential future opportunities, competitive advantages, or regulatory impacts that might alter the project's desirability. **In summary:** Given the negative NPV and low IRR relative to the cost of capital, the project is financially unattractive under current assumptions. FUN should **reject** this investment unless qualitative factors or strategic considerations justify otherwise.